Download Creation of a magnetic plasmon polariton through strong coupling between... atom and the defect state in a defective multilayer microcavity

PHYSICAL REVIEW B 77, 214302 共2008兲
Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic
atom and the defect state in a defective multilayer microcavity
D. Y. Lu,1 H. Liu,1,* T. Li,1 S. M. Wang,1 F. M. Wang,1 S. N. Zhu,1 and X. Zhang2
1
Department of Physics, National Laboratory of Solid State Microstructures, Nanjing University,
Nanjing 210093, People’s Republic of China
25130 Etcheverry Hall, Nanoscale Science and Engineering Center, University of California, Berkeley, California 94720-1740, USA
共Received 22 September 2007; published 4 June 2008兲
We studied the propagation of an electromagnetic 共EM兲 wave in a defective multilayer microcavity with an
artificial magnetic atom located at the edge of the defect layer. When the frequency of the defect state is tuned
to the resonance frequency of the magnetic atom, strong coupling happens between this atom and EM waves.
It creates a type of magnetic plasmon polariton 共MPP兲 with Rabi-type splitting effect that results in the two
branches of the MPP mode. The linewidth of the MPP and Rabi-type oscillation of magnetic field inside the
atom are investigated in the simulations. A great enhancement of local fields can also be obtained from the
MPP, which has a good application in nonlinear optics.
DOI: 10.1103/PhysRevB.77.214302
PACS number共s兲: 78.20.Ci, 73.20.Mf, 78.20.Bh
Experimental studies of atom-photon interaction have
early been carried out in the field of solid state physics and
atomic physics. They are usually realized between atoms or
quantum wells and optical media such as photonic crystals1,2
and cavities.3–9 A Rabi vacuum-field splitting effect is observed at both the atom-cavity coupling4,5 and the quantum
well–cavity interaction.9 In recent researches of metamaterials, artificial nanostructures such as nanoparticles and split
ring resonators 共SRR兲 have attracted wide study interest.
These resonant elements behave like real atoms when they
interact with electromagnetic 共EM兲 waves. Their electric or
magnetic responses play important roles in the characterization of metamaterials.10–32 The interaction between nanoparticles and photons has been studied in periodic structures by
Linden et al.11 Such a nanoparticle-photon interaction results
in selective suppressed extinction of plasmon resonance and,
by changing the array period, can be tuned continuously.
Similar coupling happens between nanowires and waveguide
modes, leading to the formation of a quasiparticle mode with
a surprisingly large Rabi splitting.12
Up to now, studies of magnetic resonances have been developed in spectra from microwave to visible
frequencies.13–32 Besides SRR,13–19 “fishnet” structures,20–23
together with nanowire pairs24–27 and stacked nanodisks,28,29
have been invented to work as magnetic resonators in the
visible range. Linden et al. reported that nanowire pairs,
viewed as magnetic atoms, can interact with each other by an
adjacent dielectric slab waveguide, giving rise to an avoided
crossing at near-infrared wavelengths.30
These coupling modes belong to new types of plasmon
polaritons that have already inspired a proliferation of experimental and theoretical research work in surface
science.31–33 In our recent paper, another kind of magnetic
plasmon polariton 共MPP兲 mode was produced in a linear
chain of SRRs, resulting from the strong exchange current
interaction between these “magnetic atoms.”34 Meanwhile,
this kind of coupled magnetic plasmon can be used to produce optical activity effect.35
In this paper, we design a configuration in which one gold
nanosandwich, viewed as a magnetic atom, is embedded into
a defective multilayer microcavity. Another type of MPP is
1098-0121/2008/77共21兲/214302共5兲
created by the strong coupling between the atom and the
defect mode of EM waves. Rabi-type splitting is observed in
this system, which results in the two branches of the MPP.
Correspondingly, Rabi-type oscillation is found in the time
domain. The change of linewidth of the MPP and its dependence on the position of the atom are also investigated in our
simulations. Great local field enhancement is realized in the
resonance region of the MPP, which has a good potential
application in nonlinear optics.
It is well known that a one-dimensional perfect periodic
multilayer possesses a forbidden band gap for the propagation of EM waves. Some allowed modes, so-called defect
states, appear inside the band gap when the symmetry of the
multilayer is disrupted.36 In Fig. 1共a兲, we construct such a
one-dimensional multilayer microcavity, which comprises
8-period alternately stacked A-B layers with one defect layer
in the middle. Layer A and the defect layer are filled with air
共n1 = 1.0兲 and layer B with a high-refraction material indium
tin oxide 共ITO, n2 = 2.0兲. To describe the geometry size of the
microcavity, we introduce a cavity parameter ␰. The thickness of A, B, and the defect layer is defined as d1 = ␰ / 共2n1兲,
d2 = ␰ / 共2n2兲, and d = ␰ / n1. For a given value of ␰, a transmission peak is obtained in the band gap for an EM wave at the
frequency ␯ = c / 共2␰兲 共c is the speed of light in vacuum兲,
which originates from the presence of a localized defect
mode inside the microcavity.
One nanosandwich, composed of two equal-sized gold
nanodisks and a middle gap, is located near the edge of the
defect layer; the middle gap parallel to the y-z plane is filled
with the same material ITO as layer B. Its geometry size is
given in Fig. 1共b兲. Such a nanosandwich acts as an artificial
magnetic atom.
FIG. 1. 共Color online兲 共a兲 Scheme of a multilayer microcavity
with a magnetic atom located at the edge of the defect layer; 共b兲
structure of the magnetic atom.
214302-1
©2008 The American Physical Society
PHYSICAL REVIEW B 77, 214302 共2008兲
LU et al.
FIG. 2. 共Color online兲 Transmission versus frequency 共with cavity parameter ␰ from 880 to 990 nm兲: 共a兲 the results of the microcavity
without atom; 共b兲 the results of the microcavity with an atom located at the edge of the defect layer.
To study the propagation property of EM waves in our
system, we perform a set of finite-difference time-domain
共FDTD兲 calculations using a commercial software package
CST Microwave Studio 共Computer Simulation Technology
GmbH, Darmstadt, Germany兲. We rely on the Drude model
to characterize the bulk metal properties. Namely, the metal
permittivity in the infrared spectral range is given by ␧共␻兲
= 1 − ␻2p / 共␻2 + i␻␻␶兲, where ␻ p is the bulk plasma frequency,
and ␻␶ is the relaxation rate. For gold, the characteristic frequencies fitted to experimental data are ␻ p = 1.37
⫻ 104 THz and ␻␶ = 40.84 THz.37
In our simulation setup, a polarized EM wave propagates
in the z direction, with its magnetic field in the y direction
and electric field in the x direction. As the cavity parameter ␰
is tuned from 880 to 990 nm, we perform transmission spectrum calculation of the microcavity without atom 关Fig. 2共a兲兴
and with an atom 关Fig. 2共b兲兴. For the microcavity without
atom, the transmission peak in the band gap is fixed at the
frequency ␯ = c / 共2␰兲 as reported before.36 For the microcavity with an atom, the transmission peak still observes the rule
␯ = c / 共2␰兲 when ␰ is far away from the value 935 nm 共outside
the blue circle: ␰ ⬎ 950 nm or ␰ ⬍ 920 nm兲. However, when
␰ approaches the value 935 nm 共inside the blue circle:
920 nmⱕ ␰ ⱕ 950 nm兲, it is surprisingly found that two
transmission peaks appear: Drifting away from ␯ = c / 共2␰兲,
one peak blueshifts to higher frequency while the other redshifts to lower frequency.
In order to explore the physical origin of these two transmission peaks, a probe is placed inside the magnetic atom to
detect the local magnetic field Hy. Variation of 兩Hy兩 versus
frequency is given in Fig. 3. Under different ␰, there are
always two peaks in each curve. When ␰ is far away from the
value 935 nm 共outside the blue circle: ␰ ⬎ 950 nm or ␰
⬍ 920 nm兲, one peak changes with ␰ according to the rule
␯ = c / 共2␰兲, which obviously comes from the defect mode of
the microcavity. The field distribution of this defect mode is
shown in Fig. 4. The other peak fixes at the frequency 160.3
THz, which comes from the magnetic resonance of the atom.
It does not change with ␰ because it is only determined by
the geometry structure of the atom. The magnetic resonance
mode is very different from the defect mode. It is confined
inside the magnetic atom and does not contribute to the
propagation property of the whole system. This can explain
why the magnetic resonance mode causes a resonant peak in
Fig. 3 but no corresponding transmission peak in Fig. 2共b兲.
In the foregoing discussions about Fig. 3, we are limited
to the results for ␰ ⬎ 950 nm and ␰ ⬍ 920 nm. When ␰ is in
the range 920 nmⱕ ␰ ⱕ 950 nm 共inside the blue circle兲, it
will be quite different: the defect mode does not comply with
the rule ␯ = c / 共2␰兲 anymore, and the magnetic resonance does
not keep at 160.3 THz either. As the defect mode is very
close to the resonance frequency of the atom, EM energy can
be exchanged between these two energy levels. Therefore,
strong coupling interaction is established between the defect
mode and the magnetic atom. This photon-atom coupling
completely changes the characters of EM modes in the microcavity. In the coupling region surrounded by the blue
circle, the resonance peaks are neither pure defect mode nor
pure magnetic resonance mode. The physical essence of this
kind of coupled photon-atom mode is a type of MPP with the
two peaks corresponding to its two branches. Basically, the
MPP is a kind of a propagation mode that can also transfer
EM energy through the system. So, the two transmission
peaks surrounded by the blue circle in Fig. 2共b兲 come from
the two branches of this MPP.
To give further evidence of the MPP, its linewidth versus
␰ is presented in Fig. 5. The linewidth of the atom is larger
than that of the defect state. In the coupling range 920 nm
ⱕ ␰ ⱕ 950 nm, the linewidth of two branches of the MPP are
between those of the atom and the defect state. As ␰ increases, the linewidth of the upper branch of the MPP 共de-
FIG. 3. 共Color online兲 Local field 兩Hy兩 detected inside the magnetic atom versus frequency 共with cavity parameter ␰ from 880 nm
to 990 nm兲.
214302-2
PHYSICAL REVIEW B 77, 214302 共2008兲
CREATION OF A MAGNETIC PLASMON POLARITON…
FIG. 4. 共Color online兲 共a兲 Electric field and 共b兲 magnetic field
distribution of the defect state in the microcavity at 170.2 THz with
␰ = 880 nm.
noted as red dotted line兲 increases from the defect state to the
atom state, while the linewidth of the lower branch of the
MPP 共denoted as black dotted line兲 decreases from the atom
state to the defect state. Therefore, in the coupling region, it
is impossible to distinguish between the atom state and the
defect state. This linewidth averaging further suggests that
the MPP is neither pure atom state nor pure defect state, but
a mixed state.
We have already demonstrated that the peak splitting in
Fig. 2共b兲 originates from the coupling effect between the
defect mode and the magnetic atom. This phenomenon is
extraordinarily similar to the Rabi splitting of energy level of
a real atom interacting with EM waves. The two branches of
the MPP in Figs. 2共b兲 and 3 can be seen as the results of
Rabi–type splitting of resonance mode of the magnetic atom.
To illustrate the splitting effect explicitly, the dependence of
the peak frequency of local field 兩Hy兩 on the cavity parameter
␰ is given in Fig. 6共a兲. The horizontal and oblique dashed
lines represent the resonance frequency of the magnetic atom
and the defect state, respectively. They intersect at ␰
= 935 nm. In the region near the crossing point 共inside the
blue circle兲, strong coupling happens and Rabi-type splitting
effect is obvious 共denoted as red arrow in the figure兲. Two
energy levels are formed in the splitting: One is above the
energy level of the atom, which is denoted as the upper
branch of the MPP; the other is below the energy level of the
atom, which is denoted as the lower branch of the MPP. For
example, for ␰ = 935 nm, the upper level is at 161.5 THz and
the lower level at 159.4 THz, thus, the energy gap 2.1 THz is
achieved.
So far, the property of the MPP is only studied in the
frequency domain. Its behavior in the time domain can also
be investigated in our simulations. After being excited by a
5-fs pulse signal, the evolution of magnetic field inside the
atom is recorded by the probe, given in Fig. 6共b兲. For a
natural two-level atom, Rabi oscillation could be established
when it interacts with a photon.38 In our system, the
nanosandwich could be seen as an artificial two-level atom if
the two resonance frequencies of the MPP in the coupling
range 关encircled by blue curve in Fig. 6共a兲兴 are taken as two
energy levels of this magnetic resonator. From Fig. 6共b兲, it is
very interesting that Rabi-type oscillation could also be real-
FIG. 5. 共Color online兲 Linewidth of the resonance peak versus
cavity parameter ␰. Black dotted line: lower branch of the MPP; red
dotted line: upper branch of the MPP. 共Dashed lines represent the
resonance linewidth of the atom and the defect state.兲
ized in our system. When excited by an EM wave, the stored
energy inside the atom is transmitted back and forth between
these two energy levels. Therefore, the Rabi-type oscillation
is observed in the evolution of local field inside the atom.
Meanwhile, its amplitude decays with time due to ohmic loss
and radiation loss, with the decay time obtained as 0.8 ps.
Above, we base our discussion on the condition that the
atom is placed at the edge of the defect layer. What will
happen if we change its position? Actually, the location of
the atom plays an important role in the coupling process.
When interacting with EM waves, the atom can be viewed as
ជ . The coupling strength is determined by
a magnetic dipole m
ជ · Bជ 共rជ兲, where Bជ 共rជ兲 is the local
the interaction energy ⌬E = −m
magnetic field of the defect mode at the atom. Therefore, to
achieve strong coupling, the atom needs to be placed at the
location where the magnetic field is enhanced most. From
the field distribution of the defect mode given in Fig. 4共b兲, it
is obvious that its magnetic field reaches maximum at the
edge and drops to zero at the center of the defect layer. The
best choice for the atom is at the edge, which is just what we
have already done. Contrarily, if the atom is placed at the
center where Bជ 共rជ兲 = 0, the interaction term will vanish, which
means no coupling interaction happens between the atom
and the defect mode. The simulation results in Figs. 6共c兲 and
6共d兲 show that Rabi-type splitting effect, as well as Rabi-type
oscillation, disappears as estimated. It provides a further confirmation that the MPP proposed in this paper is created completely through the interaction between two modes.
Finally, the MPP is also used to enhance local field in the
microcavity. Variation of the magnetic field intensity at the
atom versus ␰ is shown in Fig. 7. Our system exhibits a much
greater local field enhancement when it enters the strong
atom-photon coupling than that in the uncoupling region,
because, in the coupling range, much more EM energy is
absorbed by the atom through the mode interaction, and high
energy storage results in the great enhancement. This localization of EM energy by the MPP could serve as a possible
application in nonlinear optics.
214302-3
PHYSICAL REVIEW B 77, 214302 共2008兲
LU et al.
FIG. 6. 共Color online兲 When the atom is located at the edge of the defect layer: 共a兲 the peak frequency of local field 兩Hy兩 inside the atom
versus cavity parameter ␰; 共b兲 the evolution of magnetic field inside the atom after excited by a 5-fs pulse signal 共with ␰ = 935 nm兲. When
the atom is located at the center of the defect layer: 共c兲 the peak frequency of local field 兩Hy兩 inside the atom versus cavity parameter ␰; 共d兲
the evolution of magnetic field inside the atom after excited by a 5-fs pulse signal 共with ␰ = 935 nm兲.
In conclusion, we have demonstrated by numerical simulations that a type of MPP is created in a system of an artificial magnetic atom situated within a defective multilayer
microcavity in the same way as a system of real atoms in an
FIG. 7. 共Color online兲 Amplitude of local field inside the atom
versus cavity parameter ␰. Black dotted line: lower branch of the
MPP; red dotted line: upper branch of the MPP.
optical cavity. Transmission spectrum calculation and local
field detecting reveal its Rabi-type splitting and linewidth
averaging feature. These effects are attributed to strong coupling between the magnetic atom and the defect mode. The
upper and lower normal modes stand for the two branches of
the MPP at the coupling region. EM field localization is significantly enhanced as compared to that of the uncoupling or
weak coupling, which makes more energy gather in the
multilayer microcavity. The dependence of the MPP on the
position of the magnetic atom and field distribution in the
defect layer has also been discussed.
Our model offers a method to realize strong interaction
between a magnetic metamaterial element and EM waves
inside the microcavities. Tailoring the light-matter interaction
via proper design of the artificial atom and microcavity allows control over such important properties as Rabi-type
splitting, field localization, etc. This system will be useful for
enhancing nonlinear optical effects such as optical bistability,
laser operation, and quantum fluctuation.
This work was supported by the State Key Program for
Basic Research of China 共2004CB619003兲 and the National
Natural Science Foundation of China under Contracts No.
10534042, No. 60578034, and No. 10604029.
214302-4
PHYSICAL REVIEW B 77, 214302 共2008兲
CREATION OF A MAGNETIC PLASMON POLARITON…
*Author to whom correspondence should be addressed;
[email protected]
1
E. Yablonovitch, Phys. Rev. Lett. 58, 2059 共1987兲.
2 M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, Science 308, 1296 共2005兲.
3
E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 共1963兲.
4
M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and
H. J. Carmichael, Phys. Rev. Lett. 63, 240 共1989兲.
5 R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett.
68, 1132 共1992兲.
6 Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael,
and T. W. Mossberg, Phys. Rev. Lett. 64, 2499 共1990兲.
7
S. Haroche and D. Kleppner, Phys. Today 42 共1兲, 24 共1989兲.
8 G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A
44, 669 共1991兲.
9
C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys.
Rev. Lett. 69, 3314 共1992兲.
10
J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys.
Rev. Lett. 76, 4773 共1996兲.
11 S. Linden, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 86, 4688
共2001兲.
12 A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, Phys. Rev. Lett. 91, 183901 共2003兲.
13 J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart,
IEEE Trans. Microwave Theory Tech. 47, 2075 共1999兲.
14 D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and
S. Schultz, Phys. Rev. Lett. 84, 4184 共2000兲.
15 R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77
共2001兲.
16 T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B.
Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 共2004兲.
17 S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and
C. M. Soukoulis, Science 306, 1351 共2004兲.
18 S. Zhang, W. Fan, B. Minhas, A. Frauenglass, K. Malloy, and S.
Brueck, Phys. Rev. Lett. 94, 037402 共2005兲.
19 C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F.
Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys.
Rev. Lett. 95, 203901 共2005兲.
20
S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood,
and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 共2005兲.
21
G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S.
Linden, Science 312, 892 共2006兲.
22 G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Opt.
Lett. 32, 53 共2007兲.
23 T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu,
Phys. Rev. E 76, 016606 共2007兲.
24 V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Dracher, and A. V. Kildishev, Opt. Lett. 30, 3356
共2005兲.
25 V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, Opt. Express 11, 735 共2003兲.
26
F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang,
Phys. Rev. E 75, 016604 共2007兲.
27 F. M. Wang, H. Liu, T. Li, S. N. Zhu, and X. Zhang, Phys. Rev.
B 76, 075110 共2007兲.
28 L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll,
S. Zou, and G. C. Schatz, J. Phys. Chem. B 109, 1079 共2005兲.
29 T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and
M. Käll, Opt. Express 14, 8240 共2006兲.
30 S. Linden, M. Decker, and M. Wegener, Phys. Rev. Lett. 97,
083902 共2006兲.
31 A. D. Boardman, Electromagnetic Surface Modes 共Wiley, New
York, 1982兲.
32 E. L. Albuquerque and M. G. Cottam, Phys. Rep. 233, 67
共1993兲.
33 M. S. Kushwaha, Surf. Sci. Rep. 41, 1 共2001兲.
34 H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun,
S. N. Zhu, and X. Zhang, Phys. Rev. Lett. 97, 243902 共2006兲.
35 H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S.
N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 共2007兲.
36 B. Shi, Z. M. Jiang, and X. Wang, Opt. Lett. 26, 1194 共2001兲.
37 M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W.
Alexander, Jr., and C. A. Ward, Appl. Opt. 22, 1099 共1983兲.
38 Y. Kaluzny, P. Goy, M. Gross, J. M. Raimond, and S. Haroche,
Phys. Rev. Lett. 51, 1175 共1983兲.
214302-5